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F wave persistence - measure of alpha motor neuron excitability calculated as the number of F responses elicited divided by the number of stimuli presented. The minimal F wave latency is typically 25-32 ms in the upper extremities and 45-56 ms in the lower extremities. F wave persistence is the number of F waves obtained per the number of ...
The gradient of F is then normal to the hypersurface. Similarly, an affine algebraic hypersurface may be defined by an equation F(x 1, ..., x n) = 0, where F is a polynomial. The gradient of F is zero at a singular point of the hypersurface (this is the definition of a singular point). At a non-singular point, it is a nonzero normal vector.
The hypotheses can be weakened, as in the results of Carleson and Hunt, to f(t) e −at being L 1, provided that f be of bounded variation in a closed neighborhood of t (cf. Dini test), the value of f at t be taken to be the arithmetic mean of the left and right limits, and that the integrals be taken in the sense of Cauchy principal values.
Once a value of y is chosen, say a, then f(x,y) determines a function f a which traces a curve x 2 + ax + a 2 on the xz-plane: = + +. In this expression, a is a constant, not a variable, so f a is a function of only one real variable, that being x. Consequently, the definition of the derivative for a function of one variable applies:
where ∇y(x) represents the gradient vector of y(x), nĚ‚ is the unit normal, and ⋅ represents the inner product operator. It becomes clear that the boundary must be sufficiently smooth such that the normal derivative can exist, since, for example, at corner points on the boundary the normal vector is not well defined.
The curl of the gradient of any continuously twice-differentiable scalar field (i.e., differentiability class) is always the zero vector: =. It can be easily proved by expressing ∇ × ( ∇ φ ) {\displaystyle \nabla \times (\nabla \varphi )} in a Cartesian coordinate system with Schwarz's theorem (also called Clairaut's theorem on equality ...
The wave equation is linear in u and is left unaltered by translations in space and time. Therefore, we can generate a great variety of solutions by translating and summing spherical waves. Let φ(ξ, η, ζ) be an arbitrary function of three independent variables, and let the spherical wave form F be a delta function.
Panels (E–F) show two different wave functions that are solutions of the Schrödinger equation but not standing waves. The wave function of an initially very localized free particle. In quantum physics, a wave function (or wavefunction) is a mathematical description of the quantum state of an isolated quantum system.